Annihilation of positronium

Alekseev, A.I. (1958). Two-photon annihilation of positronium in the P-state. Sov. Phys. JETP 34 826-830. 

The 3-to-2 photon ratio technique observes the ratio of 3 versus 2 photon annihilations of positronium (and positrons). In vacuum positronium will annihilate via 3-photon decays only. Trapped inside closed pores, both annihilation paths are possible. This change can be used to detect the onset of open porosity as shown in Figure 7.2. A change in slope (the slope is shown as a solid line) occurs at about 23% porogen load, indicative of an increased likelihood for positronium to escape from the sample. 

Bell s theorem is by now a well-established experimental fact. The most accurate experiments have been based on analogs of the EPR-Bohm experiment measuring photon polarizations rather than spins of massive particles. Instead of spin-up and spin-down states, photons can have right and left circular polarizations. In certain processes, two photons with correlated polarizations—one left, one right— can be emitted in opposite directions. Wheeler had proposed in 1946 that the pair of photons emitted in the annihilation of positronium (see Fig. 7.12) were entangled with opposite polarizations. This was experimentally confirmed by Wu and Shaknov in 1949. 

Regarding the intensity, the higher value corresponds to the intermediate component, ti, which represents approximately the 90% of the total intensity. This agrees with the results obtained in previous studies carried out with porous carbons [12] and carbon fibers from mesophase pitch [11]. In the first study [12] only the intermediate component (ti) was found from the lifetime spectrum. These results indicate that, in carbon materials with high surface area, most of the positron annihilation takes place on the surface of the porosity. In the second case [11], i.e., PALS in carbon fibers, two components in the lifetime spectrum were found. The first component with high intensity (97%) and lifetime of 367 ps was attributed to positron annihilation in pores. The second one with a lifetime of 1130 ps corresponds to the annihilation of positronium atoms (i e., o-Ps). 

The energy of annihilation of positronium may be emitted as two, three, or more photons, according to the symmetry of the state which decays. Single photon emission can take place only in the presence of fields strong enough to absorb the momentum we shall not be concerned with this case. 

This inevitably leads to the annihilation of anti-particles from the bound states of protonium (Pn = pp) and positronium (Ps = e+e ). We found this reaction to be a very important mechanism for the loss of antihydrogen [26, 27, 29]. 

The lowest order contributions to the annihilation rates for the nPs1So and nPS3Si states of positronium were first calculated by Pirenne (1946)... 

Another model of positronium formation, the so-called spur model, was originally developed by Mogensen (1974) to describe positronium formation in liquids, but it has found some applications to dense gases. The basic premise of this model is that when the positron loses its last few hundred eV of kinetic energy, it creates a track, or so-called spur, in which it resides along with atoms and molecules (excited or otherwise), ions and electrons. The size of the spur is governed by the density and nature of the medium since these, loosely speaking, control the thermalization distances of the positron and the secondary electrons. It is clear that electrostatic attraction between the positron and electron(s) in the spur can result in positronium formation, which will be in competition with other processes such as ion-electron recombination, diffusion out of the spur and annihilation. 

Before the advent of low energy beams, the only means of investigating positron interactions with atoms and molecules was to study their annihilation. Information could thereby be obtained directly on the annihilation cross section but only indirectly for other processes such as elastic scattering. In this chapter we consider the annihilation of so-called free positrons in gases. The fate of positrons which have formed positronium prior to annihilation is treated in Chapter 7. 

Once the background is subtracted, the component of the spectrum due to the annihilation of ortho-positronium is usually visible (see Figure 6.5(a), curve (ii) and the fitted line (iv)). The analysis of the spectrum can now proceed, and a number of different methods have been applied to derive annihilation rates and the amplitudes of the various components. One method, introduced by Orth, Falk and Jones (1968), applies a maximum-likelihood technique to fit a double exponential function to the free-positron and ortho-positronium components (where applicable). Alternatively, the fits to the components can be made individually, if their decay rates are sufficiently well separated, by fitting to the longest component (usually ortho-positronium) first and then subtracting this from the... 

The broken-line portion of the v+/(Zeg) curve, which attains a maximum and then falls, was explained by Bose, Paul and Tsai (1981) in terms of the formation of positronium due to positron heating in the electric field, so that the apparent value of Z s) rises as the amount of positronium formation increases. At high electric fields nearly all the positrons form positronium and do not annihilate at the foil. 

In this chapter we consider the physics of the positronium atom and what is known, both theoretically and experimentally, of its interactions with other atomic and molecular species. The basic properties of positronium have been briefly mentioned in subsection 1.2.2 and will not be repeated here. Similarly, positronium production in the collisions of positrons with gases, and within and at the surface of solids, has been reviewed in section 1.5 and in Chapter 4. Some of the experimental methods, e.g. lifetime spectroscopy and angular correlation studies of the annihilation radiation, which are used to derive information on positronium interactions, have also been described previously. These will be of most relevance to the discussion in sections 7.3-7.5 on annihilation, slowing down and bound states. Techniques for the production of beams of positronium atoms were introduced in section 1.5. We describe here in more detail the method which has allowed measurements of positronium scattering cross sections to be made over a range of kinetic energies, typically from a few eV up to 100-200 eV, and the first such studies are summarized in section 7.6. 

Note that, as can be seen from the discussion in subsection 1.2.1, the contributions from the higher order annihilation modes are negligible at the present levels of precision. Thus, the rate for the annihilation of ortho-positronium into five gamma-rays is only 10-6 of that for three gamma-rays, with a similar value for the ratio of the rates for para-positronium annihilation into four and two gamma-rays. 

The basic principle of the experiment of Canter, Mills and Berko (1975) was to collide low energy positrons with a surface and to look for coincidence between a Lyman-a photon and a delayed gamma-ray arising from the subsequent annihilation of a 13S positronium. The presence of the Lyman-a signal was verified by the use of three interference filters with pass bands centred on, just above, and just below, 243 nm. An enhanced coincidence rate was found with the 243 nm filter in place. A similar Lyman-a gamma-ray technique has been adopted by all subsequent workers in this field (e.g. Laricchia et al., 1985 Hatamian, Conti and Rich, 1987 Ley et al., 1990 Schoepf et al., 1992 Steiger and Conti, 1992 Hagena et al., 1993 Day, Charlton and Laricchia, 2000). 

---